Mechanisms and Modelling of Cracking under and Fretting Conditions

Eduardo R. de 10s Rios Department of Mechan~calEngmeenng, University of Sheffield, Sheffield, UK

Corrosion Fatigue

It is well established that crack growth proceeds at a higher rate in aggressive environments than in air. This complicates even f~irtherthe prediction of fatigue life, where safety factors are required to account for these uncertainties. However, considering that these correction factors are derived fi-om projected service conditions (which are shortened in time for laboratory testing), make questioiiable the accuracy of the predictions, although designs are evaluated tlirougli service simulation tests. To increase the accuracy of the predictions it is necessary to develop models of corrosion fatigue that incoi-porate the main aspects of tlie physical phenomena. These aspects of the environineiitally assisted corrosion fatigue of metals in aqueous solutions involve clectro- cheliiical proccsscs which include anodic and cathodic reactions. The former is related to an anodic dissolution nieclianism and the latter is associated with . Several possible corrosion fatigue mechanisms related to anodic dissolut~onhave been suggested, including pitting induced crack initiation and short crack growth, fil~ii-ri~pti~rc, dissolution of slip bands at tlie crack tip and grain boimdasy oxidatioli. Of tlicse, pitting corrosion is thc most damaging and wlli be discussed next.

Pitting corrosion

Pitting is the res~rltof electrochemical reactions in local cells on the surface of a metal [I], At the site of a pit, coi-sosioii OCCU~Sat the local anode, caused by electrocheiiiical differences between one site and its surrounding area at the metal-liquid interface. Pits are usually found at the origin of in industrial machinery parts as well as on test specimens. This implies that pit initiation triggers fatigue crack initiation. Therefore, the quantitative evaluation of pitting is very mportant in the prediction of corrosion fatigue life. Pitting is a common phenoinenon occurring above the pitting potential (Ep) for low carbon steel, medium carbon steel and Al-alloys. However, pitting still occurs below Ep in some Al- alloys [2]. In the case of a low stress level and a low loading frequency, pits may play a inajor role in short fatigue crack initiation and propagation. Akid and Miller [3] observed short fatigue crack initiation at the corner of pits. When pit-depth together with the initiated short crack depth exceeded a critical length, short fatigue cracks propagated at increasing crack growth rates. An cxaiiiple of fatigue cracks initiated at pits is shown in Fig. I A model of corrosio~~fatigue was developed by de 10s Rios et. a1 [5] which considers the eCfect of I~emisphcricalpits in the initiation and pt-opagat~onof fatigue cracks. Experimental evide~icehas sliown that the d~ameterof the 11irtjor pit, which eventually created a dominant fatigue crack, ~ncreasedas a f~mctiouof time (t), i.c. 1%.

Hc - H0 = B(t- t,J<

Hc - M,, = B[(N - N,,)/f]li

Where t, (incubation time), H, critical pit size, 1-1, (mean inclusion size) and coefficient B are dctern~i~ledexperimentally. Then the number of cycles for pit growth can be calculated as:

N ,,,, =S( t,, +(H, H,)' -

Stress concentration rrro~rndan inclusion or apit

According to Weiss, Stickler and Blom [b],the field of stress concentration around an isolated micropit was found to extend to approximately twice the radius of the micropit or less. A similar analysis can be used to estimate the effective ranges of stress coilcentration for a pit. Co~isideringthe local pit stress reduces (by a power of the r-2 form) for a semi-infinite body, Equation (4) is proposed to evaluate the stress concentration as a function of distance from the pit centre.

Consequently, the local stress surrounding the pit, o,,, as a function of the distance from the original pit centre will take the following form: This stress is then used to calc~llatethe number of cycles for crack propagation employing a Paris type crack propagation law, i.e.:

Where Q, is the crack driving force, e.g. crack tip plastic displacement (CTPD), AK, etc. Thus

And total life, for a condition where pit formation is the dominant environn~entalfactor, is:

Hydrogen embrittlernent

For some metals hydrogen embrittlement plays a major role in cathodic reaction-related corrosion fatigue. There are several possible mechanisms put forward to explain hydrogen effects including:(l) a critlcal hydrogen concentration which induces decohesion, (2) hydrogen environment enhanced crack tip plasticity, (3) col-rosion product and roughness induced wake closure, and (4) hydrogen trapping induced intergranular short crack initiation and growth [7,8]. For subcritical fatigue crack propagation, the reversible local plastic flow process may be the dominant mechanism. In the case of hydrogen assisted fatigue crack growth, hydrogen would affect the plastic zone at the crack tip, consequently the effect of hydrogen on the reversible plastic flow has to be considered when applying the crack tip decohesion model. Beachem [9], on the basis of observations made after applying various degrees of deformation to a material degraded by hydrogen (particularly on the lowering of the torsional flow stress in a 1020 steel) proposed a hydrogen assisted cracking theory in which the role of hydrogen is to augment dislocation motion. The 1020 steel case seems to be associated with surface damage [lo]. Enhanced dislocation motion by hydrogen is now definitely established, with the extent of the softening being dictated by enhanced screw dislocation mobility, enhanced dislocation injection at surfaces, and the promotion of shear instabilities. Lynch [l I] proposed that some environments including hydrogen, promote crack tip dislocation nucleation and high strain localization in aluminium and iron based alloys. Lankford and Davidson [12] demonstrated that higher crack tip opening strains are responsible for the rapid growth kinetics of small fatigue cracks in aluminium alloys stressed in moist air, at least for cracks in single grains. It should be emphasized however that the suggestion of a crack tip slip-softening mechanism is based on the observation of hydrogen lowering the strength in ductile materials, while for high strength steel, hydrogen has little effect on yield strength, which is controlled by other microstructural features. For lower strength steels (o,< 700 MPa) varying effects have been found. H.Matsui, S.Moriya and H.Kimura [13] found a decrease in yield strength after electrolytic charging at large hydrogen fugacities. Similar results were also reported by Petch [14] for steels with varying carbon content up to 0.60 pct, by Lee et al [15] for spheroidized 1090 steel, by Ciaraldi et at [16] in an Al-Zn-Mg alloy. However, work hardening as opposed to softening has also been observed in many alloys.

Modelling hydrogen-assisted slzort crack growth

The inodel of Navasso-de 10s Rios [17] as extended in [18] was f~lrtherexpanded to incorporate the effect of hydrogen in short fatigue crack growth. The equat~onswhich describe the environmental-assisted fatigue process are presented first, and discussed later. The equilibrium equation of all the forces in the crack system is:

The crack tip open displacement is:

CTOD = b I: f (Lr) dx

The crack growth rate is:

d a - = A (CTPD)" dN

The diff~isionequation for hydrogen including hydrogen trapping is:

where CL 1s the lattice hydrogen concentration, Cr the trapped hydrogen concentration, and DL the concentration independent lattice diffusivity. P(C) is a function of hydrogen concentration, C(x,t), which is a complicated time-dependent f~inction,and cannot be expressed in a simple expression. Therefore the integral equilibriuin equation (9) has to be solved using the diffusion equation 12. Numerical analyses were carried out on a computer using a one-dimensional explicit differential equation with moving boundary. The moving boundary positions are determined by calculating the crack increment cycle by cycle. Further details of the inodel are given in reference [19]. Theoretical predictions and the experimental data are compared in Table 1. Because subcritical crack growth produces a fresh surface after every cycle, it was assunled that the concentration of hydrogen at the crack tip is always equal to the initial concentration Co of 0.65 atm ratio.

Table 1. The comparison of the experimental fatig~~elife with the theoretical predictions for the different stress ranges. Al-Li 8090, frequeiicy = 10 Hz, R = 0.1

Nutnber of cycles to failure Nt Stress range Experimental data Prediction 144 MPa 420,900 407,000 442,000 180 MPa 2 19,000 223,000 183,000 207 MPa 109,000 1 15,000 lO9.000

Crucks and hyr/rogen

It has bcen believed for sometime, and also proven experimentally [20], that hydrogen induced cracking (HIC) ~nitiationsites correspond to the location of the highest hydrostatic stress o{:'"".However, according to a recent investigation using SIMS (Secondary Ion Mass Spectroscopy) ~uiderdifferent ratios of 1/11 mixed mode loads [21], there are two hydrogen accumulation peaks ahead of the crack tip, i.e. hydrostatic stress induced hydrogen accun~ulation peak c;, located at tl~ccrack tip elastic-plastic boi~ndary and dislocation ii~duced(i.e. plastic strain induced) hydrogen acc~unulationpeak c:, located at the point of highest equivalent plastic strain, which in turn correspond to the point of highest dislocation dellsitql xvrery clGse tc tlte crncJ

Figure 2. Dist~~b~~t~onof Myd~ogcn conccnt~at~on ahead of sl~t(clack) In terms of these two hydrogen accumulation peaks, the site of hydrogen-induced cracks (HIC) would depend on which peak, in combination with its local maximum nonnal stress, attains the critical state first. Therefore, for a mode I slit, the hydrostatic stress induced hydrogen accumulation is dominant, and the dislocation induced hydrogen accumulation is rather weak. In this case, the c:, peak plays a more important role than the c:, peak, and consequently the HIC initiation site is determined by the location of the c;, peak (elastic- plastic boundary) Fig. 3(a). For a combined 1/11 mode loading case, however, the situation is more complicated since: (i) the HIC initiation sites are at an angle 8 with the slit direction and (ii) the HIC initiation site may relate to either c;, or c:, depending on the ratio of KII/K1as well as on the loading process. Indeed, in slow strain rate (SSR) tests, and when Kn/KI > 1, cracks did not form ahead of the notch tip but they initiated at the notch surface where the equivalent plastic strain is maxiinum (see Fig. 3(b)). Conversely, when Krl/KI< 1, HIC initiation did first appear some distance ahead of the slit tip. However, in constant load (CL) tests, the initiation site of HIC is always ahead of the notch tip and associated with the position of the cI, peak as shown in Fig. 3(c).

Figure 3. HIC ~iiltlat~onsites at (a) ~node1 notch tip; (b) combmed 1/11 inode (KII/KI= 3 I) slit tlp (111 SSRT tests), (c)comb~ned 1/11 mode (KII/KI= 3 1) slit t~p(In CLT tests)

Fretting Fatigue

Fretting occurs when two surfaces are in contact and subjected to oscillatory tangential movement. The repeated shear stresses that are generated by friction during the relative motion causes surface damage known as fretting . Moreover, surface cracks are likely to initiate in the fretting wear zone. This will eventually leads to crack growth and can result in a significant decrease in fatigue life of a material. When fretting damage is associated with decreased fatigue performance, the phenomenon is termed as fretting fatigue. Such a fatigue failure mechanism is extremely common in aircraft structural lap joints and turbineldisk contacts.

Characteristic of fretting fatigue

The mechanism of surface damage that can cause crack nucleation is complex and difficult to study. Surface damage due to wear occurs when the mating surfaces under normal load are subjected to relative movements. Damage begins with local adlicsion between the interface and progresses when adhered particles are removed fi-0111 tlie surfacc. The Sol-mation of a fretting scar is typically smaller than a nlillimetre in dcpth 1221 and they can act as micronotches, raising locally tlie stress level and providing a sitc for an emerging Catiguc crack. Thc general cl~aracteristicof fretting fatigue dainagc is shown in Figure 4.

Figure 4. Cross-scclion of a l'rctting fatigue crack. Co~~rte:

Fretting fatigue cracks grow initially at a particular angle relative to the surface which depcnds on thc frictional and applicd stresses (phase I). As tlic crack propagates inwards, the contact surface stress decrease. This may lead to crack arrest or if static or alternating stresses exist in tlie bulk of the material, the crack will change direction and r~uipespendicular to the surface as a mode I crack. The dcptli at which this occurs depends on the n~agnitudeof the surface shear stresses, which depend on the coefficient of hction and the normal contact stresses.

Fretting fatigue of aircraft materials: experimental and numerical study

Fretting fatigue cracks in meclianical joints are an ongoing problem in airfi-an~es.These cracks initiate under conditions which involve three-di~i~ei~sioilalcontact stresses between the fastener and panels and between panels themselves. Depending on the fastener system there are several locations where fktigue cracks may initiate. For example, in systems with a low or medium clainping force, the crack initiation site may occur in the miniinurn net section at the edge of the fastener holes (in tlie forni of a part-elliptical corner crack), or at the intcrsection of the countersink profile and the holc. Such crack initiation sites lead to a shorter fatigue life of the joint. For fastener systems with high clainping force, the fretting n~echanisin is dominant and cracks invariably initiate at some distance away from the fastener hole. This crack initiation site res~iltsin a substantially increased fatigue life coinpared to cracks initiated at the minilnuin net section along a row of rivet holes. Therefore, a coinprehensive study of fretting fatigue, with associated modelling, is required for the developtnent of a damage tolerance rnetliodology leading to accurate predictions of fatigue life and thence designs optiinisation of high-load transfer joints. Fretting fatigue tests using Al 2024-T35 1 specimens and steel and aluminiun~contact bridge pads, were performed with the axial load amplitude 100 MPa and various values of norii~alpressure covering the range 10-120 MPa. In all tests fidly reversed cyclic axial load was applied with a sinusoidal waveform of 20 Hz frequency. Full details of the experi~nental set up and test procedure are given in Ref. [23]. The influence of nornial load on tlie fretting fatigue life is shown in Figs. 5 and 6. These figures shows that: (i) there is a considerable reduction in fatigue strength due to fretting; (ii) the fatigue life reduces as the contact pressure increases to a critical value of the nornial load; (iii) above this nomal load further Increase 111 the normal pressure tends to increase fatigue life. Shot peening significantly increases the betting fatigue durab~lity,particularly at low contact stresses. It should be noted that the durability of peened but rough specilllens in the lnediuin range of contact pressure is higher than that of polished specimens. This correlates with other work reported in the literature, indicating that there are two beneficial effects of shot peening 111 fretting fatigue. One is the compressive residual stresses, the other being surface roughness [24] Alumiiiium bridges show a similar trend with normal pressure as for steel bridges. However, the critical normal pressure, (giving tlie shortest life) 1s achieved with a normal pressure of approximately 40 MPa using aluminium bridges while it is about 80 MPa for steel bridgcs. Furthermore, fatigue life at normal pressures above the critical point arc I~igherfor aluminium bridgcs than for steel br~dges,while the opposite is true below the critical iiormal pressure for aluminiuim bridges (see Fig. 6).

Al 2024-16 c =100MPa, R--1 Bridge span=16 5mm

7 Steel Bridge @ Aluminum Bridge

Contact Pressure, (MPa)

Figures 5 and 6. Flettlng fat~guel~fe '1s a functton of contact plcssule Stress Analysis

To predict the initial growth direction and site of fretting fatigue cracks, the fretting damage parameters need to be quantified. To examine the stress distribution on the specimen during cyclic loading, two-dimensional elastic finite element (FE) analysis was carried out under plane strain condition using the con~mercialfinite element package ANSYS. The stress distribution over the contact interface between the specimen and the bridge is shown in Fig. 7.

t - Contact Region -

i :sz.~:eCilr ie:-er,w 'n n Distance from center, x (mm)

(a) (b) Figure 7. Stress distribution over the contact area obtained from the nunierical aiialysis

Fig. 7(a) presents the tangential and shear stress distributions along the contact area when the axial cyclic stress achieved its niaxi~iiunivalue. It shows that these stresses have peak values at only one of tlie edges of the pad (leading edge). Fig. 7(b) shows the distribution of t?lr: stress rznges during cyclic a?i.iz! !~ading.It yh~ws!!?at !l?r: ra~lgeof tangentip! pnd shear stress achieve maximum value at the outer edge of the pad. Comparisons with observations ~mdefrom tlie test pieces, confisni this site as being thc primary crack initiation location. From the FE results, the variation of these stresses with angular locations below the leading edges of the bridge feet at various depths, could be investigated. The result of this investigation is sulnmarized in Fig. 8 where the orientation of peak strcsses are compared with the initial direction of crack growth obtained from the experiments. It shows that initial crack directions for both contact materials coincide with the direction the maximum value of the tangential stress range, AG~~,,,,,,. Contact Pressure (MPa)

Thc mcchal~ismsof crack initiation and failure are different between peened and unpee~led conditions in fretting fatigue. Fig. 9 summarises these diffcrences.

Unpeened specimens Low contact pressure The initiation of li-etting fatigue cracks in unpeened specimens was always in the form of 30 semi-elliptical surface cracks. At low contact pressure only one crack iriiiiaicd and PI-opagarecilo faii~~re

High contact pressure At high contact pressure, on the other hand, there was iiiulticrack initiation whicli leads to coalescence and to the early formation of a through section crack Peened specimens Low contact pressure In peened specimens, failure was associated with a single subsurface crack originating from the comer and propagating as a quarter-elliptical crack

High contact pressure Cracks initiated both at the surface and subsurface. However, all surface cracks were substantially retarded or arrested by the effect of the compressive residual stress left after shot peening 500pni -

Figure 9. Crack ~n~tiat~onpomts In frettlng fat~gue

References

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